<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<title></title>
<!--Generated on Mon Oct 27 10:48:21 2014 by LaTeXML (version 0.7.999_04) http://dlmf.nist.gov/LaTeXML/.-->

<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<link rel="stylesheet" href="../../../../../../LaTeXML.css" type="text/css">
<link rel="stylesheet" href="../../../../../../ltx-article.css" type="text/css">
<link rel="stylesheet" href="../../../../../../customRules.css" type="text/css">
</head>
<body>
<div class="ltx_page_main">
<div class="ltx_page_content">
<div class="ltx_document">
<div id="Sx1" class="ltx_section">
<h1 class="ltx_title ltx_title_section">Non-maximum suppression</h1>

<div id="Sx1.p1" class="ltx_para">
<p class="ltx_p">Our implementation of non-maximum suppression is based on morphological
gray-scale dilation <cite class="ltx_cite">[<a href="#bib.bib1" title="Image Processing, Analysis, and Machine Vision" class="ltx_ref">1</a>]</cite> defined by the formula</p>
<table id="Sx1.Ex1" class="ltx_equation">

<tr class="ltx_equation ltx_align_baseline">
<td class="ltx_eqn_pad"></td>
<td class="ltx_align_center"><img id="Sx1.Ex1.m1" class="ltx_Math" style="vertical-align:-19px" src="mi/mi10.png" width="442" height="35" alt="\left(F\oplus S\right)\left(x,y\right)=\max_{\left(x^{\prime},y^{\prime}\right%
)\in D_{S}}\left[F\left(x-x^{\prime},y-y^{\prime}\right)+S\left(x^{\prime},y^{%
\prime}\right)\right]\,,"></td>
<td class="ltx_eqn_pad"></td>
</tr>
</table>
<p class="ltx_p">where <img id="Sx1.p1.m1" class="ltx_Math" style="vertical-align:-2px" src="mi/mi2.png" width="18" height="16" alt="F"> is the filtered image, <img id="Sx1.p1.m2" class="ltx_Math" style="vertical-align:-2px" src="mi/mi12.png" width="16" height="16" alt="S"> is a structuring element, and
<img id="Sx1.p1.m3" class="ltx_Math" style="vertical-align:-5px" src="mi/mi11.png" width="29" height="18" alt="D_{S}"> is the domain of <img id="Sx1.p1.m4" class="ltx_Math" style="vertical-align:-2px" src="mi/mi12.png" width="16" height="16" alt="S">. Gray-scale dilation is a more general
approach than the method of detection of <a href="LocalMaximaDetector.html" title="" class="ltx_ref">local intensity maxima</a>,
because the structuring element can have an arbitrary form.</p>
</div>
<div id="Sx1.p2" class="ltx_para">
<p class="ltx_p">We first perform a gray-scale dilation of the filtered image <img id="Sx1.p2.m1" class="ltx_Math" style="vertical-align:-2px" src="mi/mi2.png" width="18" height="16" alt="F">
using a structuring element <img id="Sx1.p2.m2" class="ltx_Math" style="vertical-align:-2px" src="mi/mi12.png" width="16" height="16" alt="S"> of size <img id="Sx1.p2.m3" class="ltx_Math" style="vertical-align:-3px" src="mi/mi14.png" width="37" height="18" alt="l\times l"> with all entries
set to zero, where <img id="Sx1.p2.m4" class="ltx_Math" style="vertical-align:-3px" src="mi/mi13.png" width="81" height="18" alt="l=2r+1">, and <img id="Sx1.p2.m5" class="ltx_Math" style="vertical-align:-2px" src="mi/mi15.png" width="13" height="12" alt="r"> is a dilation radius given
by the user. The approximate molecular positions are extracted by
finding pixels in the image <img id="Sx1.p2.m6" class="ltx_Math" style="vertical-align:-2px" src="mi/mi2.png" width="18" height="16" alt="F"> that have intensities equal to corresponding
pixels in the dilated image and also have an intensity greater than
a user-specified <a href="Threshold.html" title="" class="ltx_ref">threshold</a>. Essentially, a
binary image is built with all non-maximum pixels set to zero and
with all local maxima set to one.</p>
</div>
<div id="Sx1.SSx1" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">See also</h2>

<div id="Sx1.SSx1.p1" class="ltx_para">
<ul id="I1" class="ltx_itemize">
<li id="I1.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i1.p1" class="ltx_para">
<p class="ltx_p"><a href="Detectors.html" title="" class="ltx_ref">Finding approximate positions of molecules</a></p>
</div>
</li>
<li id="I1.i2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i2.p1" class="ltx_para">
<p class="ltx_p"><a href="Threshold.html" title="" class="ltx_ref">Threshold selection</a></p>
</div>
</li>
</ul>
</div>
</div>
</div>
<div id="bib" class="ltx_bibliography">
<h1 class="ltx_title ltx_title_bibliography">References</h1>

<ul id="L1" class="ltx_biblist">
<li id="bib.bib1" class="ltx_bibitem ltx_bib_book">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[1]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">M. Šonka, V. Hlaváč and R. Boyle</span><span class="ltx_text ltx_bib_year">(2007)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">Image Processing, Analysis, and Machine Vision</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_edition">3rd edition edition</span>,  <span class="ltx_text ltx_bib_publisher">Cengage Learning</span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Non-maximum suppression" class="ltx_ref"><span class="ltx_text ltx_ref_title">Non-maximum suppression</span></a>.
</span>
</li>
</ul>
</div>
</div>
</div>
<div class="ltx_page_footer">
<div class="ltx_page_logo">Generated  on Mon Oct 27 10:48:21 2014 by <a href="http://dlmf.nist.gov/LaTeXML/">LaTeXML <img src="" alt="[LOGO]"></a>
</div>
</div>
</div>
</body>
</html>
